منابع مشابه
Least Squares Methods for Elliptic Systems
A weighted least squares method is given for the numerical solution of elliptic partial differential equations of Agmon-Douglis-Nirenberg type and an error analysis is provided. Some examples are given.
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Least-squares principles use artificial " energy " functionals to provide a Rayleigh-Ritz-like setting for the finite element method. These function-als are defined in terms of PDE's residuals and are not unique. We show that viable methods result from reconciliation of a mathematical setting dictated by the norm-equivalence of least-squares functionals with practicality constraints dictated by...
متن کاملLeast-squares Proper Generalised Decompositions for Elliptic Systems
Proper generalised decompositions (PGDs) are a family of methods for efficiently solving high-dimensional PDEs. Convergence of PGD algorithms can be proven provided that the weak form of the PDE can be recast as the minimisation of some energy functional. A large number of elliptic problems, such as the Stokes problem, cannot be guaranteed to converge when employing a Galerkin PGD. Least-square...
متن کاملLeast Squares for Second Order Elliptic Problems
In this paper we introduce and analyze two least squares methods for second order elliptic di erential equations with mixed boundary conditions These methods extend to problems which involve oblique derivative boundary conditions as well as nonsym metric and inde nite problems as long as the original problem has a unique solution With the methods to be developed Neumann and oblique boundary con...
متن کاملTotal least squares methods
1. the use of weighted norms as a measure of the data perturbation size, capturing prior knowledge about uncertainty in the data; 2. the addition of constraints on the perturbation to preserve the structure of the data matrix, motivated by structured data matrices occurring in signal and image processing, systems and control, and computer algebra; 3. the use of regularization in the problem for...
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ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 1985
ISSN: 0025-5718
DOI: 10.2307/2007792